Convert the base 10 real number 119. 78125 into
A. Base 2 _____________________________
B. Base 8 _____________________________
C. Base 16 ____________________________
2
119
2
59
.78125
x 2
1
2
29
1
2
14
1
2
7
0
2
3
1
2
1
1
1
.5625
x 2
1
.125
x 2
0
.250
x 2
0
.5
x 2
2
0
1
1
1
1
1
0
1
1
1 . 1
1
.000000000
0
0
1
15 POINTS
1. Convert the base 10 real number 119. 78125 into
64
0
1
32
1
16
1
0
4
2
1
.5
1
1
1 . 1
.25
1
.03125
0
0
1
0
0
0
A. Base 2 ____________________________________________________________
1 6 7 . 6 2
B. Base 8 _____________________________
C. Base 16 ____________________________
15 POINTS
1. Convert the base 10 real number 119. 78125 into
64
0
1
32
1
16
1
0
4
2
1
.5
1
1
1 . 1
.25
1
.03125
0
0
1
0
0
0
A. Base 2 ____________________________________________________________
B. Base 8 _____________________________
7 7 . C 8
C. Base 16 ____________________________
As you can see below, the following code beginning at the label main: pushes
two arguments in the form of simple 2s complement integers on the stack and
then calls a label named max:. You must write the code at the label named
max: as a function, using our conventions of expecting arguments on the
stack and returning a result in the AC. Of course the max: function you must
write must return the larger of the two arguments passed to it on the
stack, or the common value if the arguments happen to be the same value.
You can see that the code at main: sets up the stack for the call to max: ,
makes the call, and then stores the value that is in the AC after the call into
the memory location labeled opres:
op1: <any 16 bit 2s complement value>
op2: <any 16 bit 2s complement value>
opres: 0
MAX:
.LOC 50
main: lodd op1:
push
lodd op2:
push
call max:
insp 2
OP1BIG:
stod opres:
halt
LODL
SUBL
JNEG
LODL
RETN
LODL
RETN
1 ;OP2
2 ;OP2-OP1
OP1BIG:
1
;OP2
2
;OP1
max:
 write the max function
For the following 16 bit sequence:
1 111 111 110 010 101
A. What is the base 10 value if the sequence is a signed 2's
complement integer ??
2 + 8 + 32 + 64 + 1  -107
B. Add the following 2's complement 16 bit sequence to the sequence
shown in part A. above, and express the answer as a base 10
signed value:
1 + 4 + 8 + 64  +77
0 000 000 001 001 101
-107 + 77  -30
1 111 111 110 010 101
0 000 000 001 001 101
----------------------1 111 111 111 100 010
1 + 4 + 8 + 16 + 1  -30
Given the following 32 bit sequence:
0
sign
1000011010111000000000000000000
exponent and mantissa components
A. If the sequence represents a signed magnitude floating point value
using the IBM format discussed in class, what is the base 10
floating point value of the sequence ??
0 1000011 0101110---0
+ 67: +3 2-2+2-4+2-5+2-6
16+3
2+12210+28+27+26  1472
B. If the sequence represents a signed magnitude floating point value
using the IEEE 754 single precision format discussed in class,
what is the base 10 floating point value of the sequence ??
0 10000110 101110---0
27
1+2-1+2-3+2-4+2-5
 27+26+24+23+22  220
The following bit string represents an IEEE 754 floating point value called Float
1. You must add to Float 1 the base 10 number shown as Float 2 (you’ll have
to convert it to a bit pattern first ):
Float 1: 0 1 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Float 2: .812510
A. Show the IEEE 754 floating point bit representation of the sum
of these two numbers
Float 1: 0 1 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  13.75
Float 2: .812510
.8125 
. 1. 1 0 1
A. Show the IEEE 754 floating point bit representation of Float 2 before
shifting:
0 0 1 1 1 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
B. Show the IEEE 754 floating point bit representation of Float 1 and
Float 2 after shifting:
HB 1
Float 1
0 1 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
HB 0
Float 2
0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
HB 1 1 1 0 1 0 0 1
C. Show the IEEE 754 floating point bit representation of the final
normalized sum of Float 1 and Float 2
HB 1 Sum of Float 1 and Float 2
0 1 0 0 0 0 0 1 0 1 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
D. What is the base 10 value of the sum of these two numbers ?
13.75 + .8125 = 14.5625
23 *(20 + 2-1 + 2-2 + 2-4 + 2-7)
= 8 + 4 + 2 + .5 + .0625
List the values in r0:, r1:, r2:, r3:, and r4: after the following program
executes from main: to the halt instruction:
0
1
2
3
4
5
6
7
8
9
10
c1:
c3:
index:
r0:
r1:
r2:
r3:
r4:
main:
1
3  6, 12, 24, 48, 96
5
0  6
0  12
0  24
0  48
0  96
lodd index:
jzer done:
subd c1:
stod index:
lodd c3:
addd c3:
stod c3:
smc1: stod r0: store at: 3, 4, 5, 6, 7
lodd smc1:
addd c1:
stod smc1:
jump main:
done: halt
Self modifying code
Write in the final values of r0:, r1:, r2:, r3:, and r4: below:
Write a routine named MySub: which will subtract two positive only 16 bit 2s
complement numbers passed as value arguments, and will place the result
back into memory at the location pointed to by a third argument (which is an
address, not a value). The routine itself should return a value of 0 if the result is
positive, and -1 if the result is negative. Just show the subroutine, not the
calling code. Assume that when the call to your routine is made the arguments are
passed on the stack such that:
SP points to the location that holds the return PC
SP+1 points to the location that holds the result address
SP+2 points to the location that holds the minuend (top number)
SP+3 points to the location that holds the subtrahend (bottom
number)
MySub:
 write
required
code
Write a routine named MySub: which will subtract two positive only 16 bit 2s
complement numbers passed as value arguments, and will place the result
back into memory at the location pointed to by a third argument (which is an
address, not a value). The routine itself should return a value of 0 if the result is
positive, and -1 if the result is negative. Just show the subroutine, not the
calling code. Assume that when the call to your routine is made the arguments are
passed on the stack such that:
SP
SP+1
SP+2
SP+3
points
points
points
points
to
to
to
to
the
the
the
the
location
location
location
location
MySub:
neg:
cn1:
lodl
subl
push
jneg
lodl
popi
loco
retn
lodl
popi
lodd
retn
-1
2
3
neg:
2
0
2
cn1:
that
that
that
that
holds
holds
holds
holds
the
the
the
the
return PC
result address
minuend (top number)
subtrahend (bottom
number)
The following bit string represents an IEEE 754 single precision floating
point number:
FLOAT: 1 0 1 1 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
A.
Show the bit string after the number it represents
has been divided by the base 10 number 128
B. The floating point number shown above can be written in hex as:
0x BFA00000
If this value was stored in a computer system’s memory byte by
byte as shown below beginning at memory address 300, explain what
type of endian storage this system has.
BF
A0
00
00
Address 300
Address 301
Address 302
Etc.
The MIC-1 bit format is shown below. You should be familiar with all the fields
and how they are used. Also below are 5 MAL instructions. Indicate if a given
MAL is valid or invalid for MIC-1, and, if valid, fill in the DECIMAL (i.e. bits
1101 are filled as 13) values for each field in the space provided.
Register designations are as follows:
pc=0 (prog counter) ac=1 (accumulator) sp=2 (stack ptr) ir=3 (instr reg)
tir=4 (tmp inst reg) zr=5 (fixed zero) po=6 (plus 1)
no=7 (minus 1)
amask=8 (addr msk) smask=9 (stack msk)
a=10(a scratch) b=11(b scratch)
c=12(c scratch)
d=13(d scratch)
e=14(e scratch) f=15(f scratch)
A. pc := pc + 255;mar := pc;rd;
B. ac := inv(mbr);mar := inv(mbr);wr;
C. tir := lshift(band(tir,mbr));if n then goto 150;
D. mbr := lshift(band(ir,amask));ir := lshift(band(ir,amask));goto 0;wr;
E.
b := ir - ac;mar := ac;if z then goto 158;
A
C
M
O
A
M
M
E
U
N
L
S
B
A
R
W
N
VALID ?
X
D
U
H
R
R
D
D
C
C
B
A
ADDR
---------------------------------------------------------------------|
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---------------------------------------------------------------------|
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---------------------------------------------------------------------|
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---------------------------------------------------------------------|
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---------------------------------------------------------------------AMUX
COND
ALU
SH
MBR,MAR,RD,WR,ENC
A latch
0 = no jmp
0 = A + B
0 = no shift
0 = no
MBR
1 = jmp if n=1
1 = A and B 1 = shift rt
1 = yes
2 = jmp if z=1
2 = A
2 = shift lt
3 = always jmp
3 = not A
Register designations are as follows:
pc=0 (prog counter) ac=1 (accumulator) sp=2 (stack ptr) ir=3 (instr reg)
no=7 (minus 1)
tir=4 (tmp inst reg) zr=5 (fixed zero) po=6 (plus 1)
amask=8 (addr msk) smask=9 (stack msk)
a=10(a scratch) b=11(b scratch)
c=12(c scratch)
d=13(d scratch)
e=14(e scratch) f=15(f scratch)
A. pc := pc + 255;mar := pc;rd;
B. ac := inv(mbr);mar := inv(mbr);wr;
C. tir := lshift(band(tir,mbr));if n then goto 150;
D. mbr := lshift(band(ir,amask));ir := lshift(band(ir,amask));goto 0;wr;
E.
b := ir - ac;mar := ac;if z then goto 158;
A
C
M
O
A
M
M
E
U
N
L
S
B
A
R
W
N
MAL
VALID ?
X
D
U
H
R
R
D
R
C
C
B
A
ADDR
-------------------------------------------------------------------------| A |
yes
| 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 9 |
|
-------------------------------------------------------------------------| B |
no
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-------------------------------------------------------------------------| C |
yes
| 1 | 1 | 1 | 2 | 0 | 0 | 0 | 0 | 1 | 4 | 4 |
| 150 |
-------------------------------------------------------------------------| D |
yes
| 0 | 3 | 1 | 2 | 1 | 0 | 0 | 1 | 1 | 3 | 8 | 3 | 0 |
-------------------------------------------------------------------------| E |
no
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-------------------------------------------------------------------------AMUX
COND
ALU
SH
MBR,MAR,RD,WR,ENC
0 = A latch
0 = no jmp
0 = A + B
0 = no shift
0 = no
1 = MBR
1 = jmp if n=1
1 = A and B 1 = shift rt
1 = yes
2 = jmp if z=1
2 = A
2 = shift lt
3 = always jmp
3 = not A
For the base 10 real number 107.21875
107
2 101
2 50
2 25
2 12
2 6
2 3
2 1
2 0
1
0
1
0
0
1
1
.
21875
0
0
1
1
1
.21875
x2
.4375
x2
.875
x2
.75
x2
.5
x2
.0
0 1 1 0 0 1 0 1 . 0 0 1 1 1
0 1 1 0 0 1 0 1 . 0 0 1 1 1
IEEE 754 shift 6 places, increase zero (ex 127) exponent by 6
IBM shift 8 places, increase zero (ex 64) exponent by 2
15 POINTS
1. For the base 10 real number 107.21875
A. Show the IEEE 754 32 bit normalized floating point bit representation
0 1 0 0 0 0 1 0 1 1 0 0 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0
B. Show the IBM 32 bit normalized floating point bit representation
0 1 0 0 0 0 1 0 0 1 1 0 0 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0
C. Show the IEEE 754 32 bit normalized floating point bit representation of
the number after it has been multiplied by 32
0 1 0 0 0 1 0 1 0 1 0 0 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0